Letter to Don Zagier by A.N. Parshin

The Density of Tunneling and Vibrational States of Glasses within the Soft-Potential Model

“…At the peak frequency, this implies a factor of six longer relaxation times for vitreous silica and a factor 1.4 longer relaxation times for the soft modes in amorphous selenium, respectively. The same values can be calculated directly using a relation derived from the golden rule [41]. So from the point of view of the interaction with the sound waves, the soft modes should be again reasonably well defined in this high-frequency range.…”

Correlated random band matrices: Localization-delocalization transitions

“…Critical states ψ(r) are characterized by having a multifractal distribution of its squared amplitudes prob(r) ≡ |ψ(r)| 2 . This spectrum becomes independent of system size and is universal for all of the critical states in the thermodynamic limit (for a review see [24]) or, more generally, follows a universal distribution ( see [25]).…”

“…It is not obvious, that the order of these different procedures commutes since the exponent fluctuates from state to state. The question about the self-averaging of the fractal exponents was recently addressed in [25] and it was claimed that exponents follow a universal scale independent distribution function in the thermodynamic limit, rather than being self-averaging. We do not investigate this question here.…”

Improving the Corrosion Resistance of Polished Stainless Steel Parts by Introducing the Energy of the Ultrasonic Field into the Forming Zone

“…Despite the constant struggle against corrosion damage, at least 40 % of the total number of equipment failures of nuclear power plants (NPP) occurs due to corrosion damage during exploitation. [1] Corrosion-resistant steels, as one of the most common structural materials, are widely used for the production of important parts of nuclear power machines and equipment operating in aggressive environments. Alloying corrosion-resistant steels with titanium and niobium, while reducing the percentage of carbon and rationally choosing the temperature range of quenching, has almost exhausted the resources for increasing intergranular corrosion (IGC) -a special, very dangerous type of corrosion destruction of metal along the boundaries of austenite grains, when the electrochemical potential of their boundary sections decreases due to the depletion by chromium.…”